Asynchronous Algorithmic Alignment with Cocycles

TL;DR

This paper introduces an asynchronous approach to graph neural networks that separates node state updates from message passing, improving efficiency and robustness in learning dynamic programming algorithms.

Contribution

It proposes a novel mathematical framework for asynchronous GNN computation, enabling scalable and invariant GNN layers under asynchronous conditions.

Findings

Asynchronous GNN layers are more efficient for dynamic programming tasks.

The proposed framework ensures invariance under various asynchronous execution models.

Practical implementations demonstrate improved scalability and robustness.

Abstract

State-of-the-art neural algorithmic reasoners make use of message passing in graph neural networks (GNNs). But typical GNNs blur the distinction between the definition and invocation of the message function, forcing a node to send messages to its neighbours at every layer, synchronously. When applying GNNs to learn to execute dynamic programming algorithms, however, on most steps only a handful of the nodes would have meaningful updates to send. One, hence, runs the risk of inefficiencies by sending too much irrelevant data across the graph. But more importantly, many intermediate GNN steps have to learn the identity functions, which is a non-trivial learning problem. In this work, we explicitly separate the concepts of node state update and message function invocation. With this separation, we obtain a mathematical formulation that allows us to reason about asynchronous computation in both algorithms and neural networks. Our analysis yields several practical implementations of synchronous scalable GNN layers that are provably invariant under various forms of asynchrony.